Ed Moloney has written to US senator John Kerry calling for an investigation into the alleged spying. Photograph: John Stillwell/PA

The American and Irish governments have been challenged to investigate an alleged spying operation directed at a family at the centre of the Boston College-IRA archive controversy that led to Gerry Adams' arrest in April.

Ireland's prime minister Enda Kenny and the US secretary of state John Kerry have received letters from the Belfast Project's director urging them to back a thorough criminal inquiry into claims that private communications from an American citizen and the US embassy in Dublin were illegally intercepted.

American-born Carrie McIntyre's husband, an ex-IRA prisoner, recorded the taped testimonies of Irish republicans for the Belfast Project. She has made a formal complaint to the Garda Síochána about how her private messages to US diplomats ended up in an Irish Sunday tabloid last month.

Ed Moloney, the Belfast Project's director, has also written letters to the leader of the Irish Republic's main opposition party Fianna Fáil and a powerful US senator calling on them to back an investigation on both sides of the Atlantic into how Carrie McIntyre's communications were made public.

In his letter to Kerry, Moloney states that "while we do not know for certain sources that I trust strongly suggest the involvement of a proscribed organisation rather than an agency of the Irish state".

Moloney points out to Barack Obama's peace envoy to the Middle East that he has also called on the Irish premier to support a trans-Atlantic criminal investigation into the spying claims.

"I believe that this is part of a mounting campaign of threat, menace and intimidation of the McIntyres. I fear for their safety and wellbeing and I expressed the hope that the prime minister would leave no stone unturned in the search for those responsible."

And in his letter to the taoiseach, Moloney says: "I am writing to ask you to leave no stone unturned in the search for those responsible and in the effort to make them amenable under the law. Tapping the phones of Irish citizens in any circumstances is unpleasant and offensive even when it is carried out within the law by legitimate agencies. But when it is done by illegal organisations and involves intercepting communications by an important ally it is, I am sure you will agree, a direct challenge to the authority of the state."

The award-winning journalist and world authority on the IRA has also written to senator Robert Menendez, the chairman of the US Senate's foreign relations committee, and Fianna Fáil leader Micheal Martin about the alleged spying operation on Irish soil.

The Sunday World newspaper last month reported that McIntyre had written to the embassy and the US consulate in Belfast seeking political asylum for herself, her children and her husband. She has denied reports that her family are seeking asylum and that she ever worked on the Boston College project.

McIntyre told the Guardian she had made no contacts with the paper and would be prepared to bring forward a large number of friends and acquaintances who would sign legal documents stating they had no knowledge of her communications with the US embassy in Dublin, let alone spoke to any newspaper about them.

There is no suggestion whatsoever that the Sunday World itself carried out any illegal hacking or act of interception regarding Carrie McIntyre's communications with US diplomatic staff in Ireland.

Her husband Anthony recorded and collated the testimonies of dozens of former IRA activists, some of whom have claimed on tape that Adams ordered the death and secret disappearance of Jean McConville in 1972. The Sinn Féin president has always denied any involvement in the kidnapping, killing and covert burial of the widow, whom the IRA accused of being an informer for the British army. Among those who accused Adams of playing a central role in the McConville murder scandal was the late Brendan Hughes, the former Belfast IRA commander whose taped testimony has been made public.

Since Adams's arrest in connection with the McConville murder, McIntyre and Moloney have faced sustained verbal attacks. Sinn Féin councillors and their supporters have labelled them "Boston College touts" – a euphemism for informers.